Details

sample180.0ms

Algorithm

intervals

Results

104.0ms

256×

body

valid

simplify635.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	177
7	177
6	168
5	143
4	100
3	59
2	34
1	17
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.0b	(- (* x x) (* (* y 4.0) y))
29.8b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

19.0ms	(+ (* x x) (* (* y 4.0) y))
17.0ms	(- (* x x) (* (* y 4.0) y))
112.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series531.0ms

Counts

3 → 9

Calls

3 calls:

318.0ms	(+ (* x x) (* (* y 4.0) y))
86.0ms	(- (* x x) (* (* y 4.0) y))
127.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify13.3s

Counts

64 → 64

Iterations

Iter	Nodes
done	5056
3	4264
2	854
1	246
0	87

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize204.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
20.2b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
22.8b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
7×	`times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`pow1` `prod-exp` `cbrt-unprod` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `clear-num` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 79

Calls

4 calls:

45.0ms	(+ (* x x) (* (* y 4.0) y))
208.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
34.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
107.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (* x x) (* (* y 4.0) y))
222.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
262.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
129.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify6.4s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1848
1	451
0	142

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize160.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (* y 4.0) (sqrt (+ (* x x) (* (* y 4.0) y)))) (/ y (sqrt (+ (* x x) (* (* y 4.0) y)))))
20.2b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
28.4b	(sqrt (+ (* x x) (* (* y 4.0) y)))
28.4b	(sqrt (+ (* x x) (* (* y 4.0) y)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`add-exp-log` `add-cbrt-cube`
29×	`times-frac`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
19×	`sqrt-prod`
12×	`associate-l`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`pow1` `sqrt-div`
6×	`associate-/r/`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 116

Calls

4 calls:

143.0ms	(* (/ (* y 4.0) (sqrt (+ (* x x) (* (* y 4.0) y)))) (/ y (sqrt (+ (* x x) (* (* y 4.0) y)))))
45.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
25.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))

series1.2s

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (/ (* y 4.0) (sqrt (+ (* x x) (* (* y 4.0) y)))) (/ y (sqrt (+ (* x x) (* (* y 4.0) y)))))
268.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
516.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
149.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))

simplify5.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	2543
1	600
0	187

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize70.0ms

Local error

Found 4 expressions with local error:

9.5b	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
20.2b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
20.2b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
22.8b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-/r*` `sqrt-prod`
8×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
5×	`pow1` `prod-exp` `cbrt-unprod`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l*`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 92

Calls

4 calls:

23.0ms	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
30.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
145.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
78.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
125.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
93.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
182.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify7.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5011
2	1484
1	370
0	127

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes464.0ms

Accuracy

53.4% (14.4b remaining)

Error of 14.8b against oracle of 0.4b and baseline of 31.4b

bsearch490.0ms

Steps

Iters	Range		Point
3	7.789660942933776e+102	1.051930614453769e+103	1.0275620942826353e+103
9	5.347374519482908e+72	1.0345609728310515e+79	5.419438360639095e+72
9	3.73636363912113e+55	6.757399575956964e+60	4.117086201251835e+60
8	2.5839679515350884e-125	7.533563991116118e-123	4.4279729591410875e-125
10	-8.380652639018829e+71	-6.542924687516393e+55	-1.3024737343616896e+64

simplify14.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8000×

body

valid